Vacuum energy in the presence of a magnetic string with delta function profile

TL;DR

This paper calculates the vacuum energy of massive scalar and spinor fields around a magnetic string with a delta function profile, revealing how the energy varies with the string's radius and potential strength.

Contribution

It introduces a detailed analytical and numerical approach to evaluate vacuum energy in a magnetic string background with delta function potential, including heat kernel and Jost function methods.

Findings

Vacuum energy sign changes with string radius.

No logarithmic divergence as radius approaches zero.

Energy behavior differs from other profiles due to heat kernel coefficient.

Abstract

We present a calculation of the ground state energy of massive spinor fields and massive scalar fields in the background of an inhomogeneous magnetic string with potential given by a delta function. The zeta functional regularization is used and the lowest heat kernel coefficients are calculated. The rest of the analytical calculation adopts the Jost function formalism. In the numerical part of the work the renormalized vacuum energy as a function of the radius $R$ of the string is calculated and plotted for various values of the strength of the potential. The sign of the energy is found to change with the radius. For both scalar and spinor fields the renormalized energy shows no logarithmic behaviour in the limit $R\to 0$, as was expected from the vanishing of the heat kernel coefficient $A_2$, which is not zero for other types of profiles.